Search results for "model [interaction]"

Uniform estimates for the local restriction of the Fourier transform to curves

2013

We prove sharp estimates, with respect to the ane arclength measure, for the restriction of the Fourier transform to a class of curves in R^d that includes curves of nite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results. Peer reviewed

Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation

2016

Abstract In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

Quasi *-algebras of measurable operators

2009

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a finite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra $(\X,\Ao)$ possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.

Krasnosel'skiĭ-Schaefer type method in the existence problems

2019

We consider a general integral equation satisfying algebraic conditions in a Banach space. Using Krasnosel'skii-Schaefer type method and technical assumptions, we prove an existence theorem producing a periodic solution of some nonlinear integral equation.

Boundedness of composition operators in holomorphic Hölder type spaces

2021

Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem

2020

We prove an analogue for algebraic stacks of Hermite-Minkowski's finiteness theorem from algebraic number theory, and establish a Chevalley-Weil type theorem for integral points on stacks. As an application of our results, we prove analogues of the Shafarevich conjecture for some surfaces of general type.

Characteristic numbers of non‐autonomous emden‐fowler type equations

2006

We consider the Emden‐Fowler equation x” = ‐q(t)|x|2εx, ε > 0, in the interval [a,b]. The coefficient q(t) is a positive valued continuous function. The Nehari characteristic number An associated with the Emden‐Fowler equation coincides with a minimal value of the functional [] over all solutions of the boundary value problem x” = ‐q(t)|x|2εx, x(a) = x(b) = 0, x(t) has exactly (n ‐ 1) zeros in (a, b). The respective solution is called the Nehari solution. We construct an example which shows that the Nehari extremal problem may have more than one solution. First Published Online: 14 Oct 2010

Comments on the validity of a common category of constitutive equations

1974

Many constitutive equations for viscoelastic materials which have appeared in the literature are modifications of the linear viscoelasticity model. Their general form is: [5] $$\tau = \int\limits_0^\infty {(f_1 C + f_2 C^{ - 1)} ds.} $$ The memory functionsf 1 andf 2, are assumed to depend explicitly on either some instantaneous or some timeaveraged value of the invariants of the rate of strain. It is shown in this paper that the general theory of simple fluids with fading memory is based on certain assumptions of smoothness for the constitutive functional which are violated by constitutive equations of the type discussed. This implies that, should any real material obey eq. [5], with an ex…

Total curvatures of compact complex submanifolds in $$C/P^n$$

1995

LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).

Finiteness properties of pseudo-hyperbolic varieties

2019

Motivated by Lang-Vojta's conjecture, we show that the set of dominant rational self-maps of an algebraic variety over a number field with only finitely many rational points in any given number field is finite by combining Amerik's theorem for dynamical systems of infinite order with properties of Prokhorov-Shramov's notion of quasi-minimal models. We also prove a similar result in the geometric setting by using again Amerik's theorem and Prokhorov-Shramov's notion of quasi-minimal model, but also Weil's regularization theorem for birational self-maps and properties of dynamical degrees. Furthermore, in the geometric setting, we obtain an analogue of Kobayashi-Ochiai's finiteness result for…